The champs have a speed stat. The champ with the highest speed goes first. Teampower is irrelevant to that. Stats like attack and defense will go into teampower as well, you can't see if a team with high teampower has high speed or not.

A lot of players use a champ like 30 day log-in reward High Khatun with a lot of speed-gear, so she goes first. High Khatun has a skill that increases the turnmeter of the team, so if their High Khatun goes first, probably the whole team will do so.

You will also see a yellow bar below the health bar. This is Turn, fill it and you get a turn

Speed will allow you to fill this bar quicker. There are also other mechanics  in the game that affect this yellow bar. "Turn control mechanics" these skills and abilities which some champions have and others do not will also affect when a player gets a turn by either  increasing or decreasing this yellow bar

Its a very strategic game with tons of variables to understand and learn how to use for maximum effect